Classifications and existence of positive solutions of higher order nonlinear iterative functional differential equations

Classification schemes for eventually positive solutions of a class of higher-order nonlinear iterative functional differential equations of the form(r(t)x(m−1)(t))′+f(t,x(t),x(Δ(t,x(t))))=0in the case when ∫∞ds/r(s)=∞ are given in terms of their magnitudes, and necessary as well as sufficient conditions for the existence of these positive solutions are also provided.